I have my own part time computer repair business and fortunately I've been very steadily busy the last few months. I've been doing this for about 15 years only by word of mouth but I've recently made up some business cards to hand out to new customers for them to hand out to friends and relatives.
As far as getting customers, you just have to get your name out there by performing good service and not ripping anyone off. The closest major computer repair place is geek squad/best buy(major ripoff company) about 30 minutes away so I get all the ones that live by me.
It all depends on where you live at and how busy you'll be or how far you want to travel as I do house calls since I do everything from my home if it requires extensive repairs or troubleshooting. However, most of my house calls are malware related and we all know a lot of computer users don't know how to surf safely and will click on anything.
The only major advice I can give you is to advertise, advertise, advertise. Make up some business cards and put up in stores, laundromats, anywhere people go.